“No human mind is capable of
grasping in its entirety the meaning of
any considerable quantity of numerical
data. We want to be able to express all
the relevant information contained in the
mass by means of comparatively few
numerical values. This is a purely
practical need which the science of
statistics is able to some extent to
meet” (Fisher, 1950 p 7).
Measures of Central Tendency
Requirements of good measures of central tendency
mean, median, mode
skewness of distribution
relation between mean, median,mode
Introduction to Statistics - Basic concepts
- How to be a good doctor - A step in Health promotion
- By Ibrahim A. Abdelhaleem - Zagazig Medical Research Society (ZMRS)
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“No human mind is capable of
grasping in its entirety the meaning of
any considerable quantity of numerical
data. We want to be able to express all
the relevant information contained in the
mass by means of comparatively few
numerical values. This is a purely
practical need which the science of
statistics is able to some extent to
meet” (Fisher, 1950 p 7).
Measures of Central Tendency
Requirements of good measures of central tendency
mean, median, mode
skewness of distribution
relation between mean, median,mode
Introduction to Statistics - Basic concepts
- How to be a good doctor - A step in Health promotion
- By Ibrahim A. Abdelhaleem - Zagazig Medical Research Society (ZMRS)
Find best statistics experts to do your Business Statistics Assignments. Just send us an email at support@homeworkguru.com with your homework assignment and we will help you with the best statistics resources available online.
If you happen to like this powerpoint, you may contact me at flippedchannel@gmail.com
I offer some educational services like:
-powerpoint presentation maker
-grammarian
-content creator
-layout designer
Subscribe to our online platforms:
FlippED Channel (Youtube)
http://bit.ly/FlippEDChannel
LET in the NET (facebook)
http://bit.ly/LETndNET
Présentation du projet Smart Cities de Belfius, dans le cadre de la Mission exploratoire AWEX-WBI: Cap sur les Villes intelligentes françaises. (Volet Strasbourg-Issy-les-Moulineaux : du 19 au 23 octobre 2015).
Frequency distribution, central tendency, measures of dispersionDhwani Shah
The presentation explains the theory of what is Frequency distribution, central tendency, measures of dispersion. It also has numericals on how to find CT for grouped and ungrouped data.
Median
Middle value in a distribution is known as Median.
Calculation of median.
1. Calculation of median in a series of individual observations or Calculation of median for ungrouped data
2. Calculation of median for grouped data
a) Calculation of median in a discrete series.
b) Calculation of median in a continuous series.
c) Calculation of median in unequal class intervals.
d) Calculation of median in open-end classes.
Merits and Demerits of Median.
Adjusting primitives for graph : SHORT REPORT / NOTESSubhajit Sahu
Graph algorithms, like PageRank Compressed Sparse Row (CSR) is an adjacency-list based graph representation that is
Multiply with different modes (map)
1. Performance of sequential execution based vs OpenMP based vector multiply.
2. Comparing various launch configs for CUDA based vector multiply.
Sum with different storage types (reduce)
1. Performance of vector element sum using float vs bfloat16 as the storage type.
Sum with different modes (reduce)
1. Performance of sequential execution based vs OpenMP based vector element sum.
2. Performance of memcpy vs in-place based CUDA based vector element sum.
3. Comparing various launch configs for CUDA based vector element sum (memcpy).
4. Comparing various launch configs for CUDA based vector element sum (in-place).
Sum with in-place strategies of CUDA mode (reduce)
1. Comparing various launch configs for CUDA based vector element sum (in-place).
Levelwise PageRank with Loop-Based Dead End Handling Strategy : SHORT REPORT ...Subhajit Sahu
Abstract — Levelwise PageRank is an alternative method of PageRank computation which decomposes the input graph into a directed acyclic block-graph of strongly connected components, and processes them in topological order, one level at a time. This enables calculation for ranks in a distributed fashion without per-iteration communication, unlike the standard method where all vertices are processed in each iteration. It however comes with a precondition of the absence of dead ends in the input graph. Here, the native non-distributed performance of Levelwise PageRank was compared against Monolithic PageRank on a CPU as well as a GPU. To ensure a fair comparison, Monolithic PageRank was also performed on a graph where vertices were split by components. Results indicate that Levelwise PageRank is about as fast as Monolithic PageRank on the CPU, but quite a bit slower on the GPU. Slowdown on the GPU is likely caused by a large submission of small workloads, and expected to be non-issue when the computation is performed on massive graphs.
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2. Statistics is the study of the collection, organization,
analysis, interpretation, and presentation of data. It
deals with all aspects of this, including the planning
of data collection in terms of the design
of surveys and experiments.
A statistician is someone who is particularly well
versed in the ways of thinking necessary for the
successful application of statistical analysis. Such
people have often gained this experience through
working in any of a wide number of fields. There is
also a discipline called mathematical statistics that
studies statistics mathematically.
3. The mean is the average of the numbers: a calculated
"central" value of a set of numbers.
There are three methods to calculate out mean and these
are:-
4. LIMITATION:- Disadvantage of the mean: The major
disadvantage, which does not always occur, is the fact that a mean
can be dramatically affected by outliers in the set. For example, if
we find the mean of the set of numbers 1, 2, 3, 4, 5 we get 3.
However, when we dramatically alter one number in the set and
find the average again, the mean is quite different. For example 1,
2, 3, 4, 20 has a mean of 6.
Uses:- The mean to describe the middle of a set of data
that does not have an outlier.
5. Example:-
A class teacher has the following absentee
record of 40 students of a class for the whole
term. Find the mean number of days a student
was absent.
Number of
days
0 − 6 6 − 10 10 − 14 14 − 20 20 − 28 28 −
38
38 − 40
Number of
students
11 10 7 4 4 3 1
6. To find the class mark of each interval, the following
relation is used.
Taking 17 as assumed mean (a), di and fidi are calculated as
follows.
Solution:-
Number of days Number of
students fi
xi di = xi − 17 fidi
0 − 6 11 3 − 14 − 154
6 − 10 10 8 − 9 − 90
10 − 14 7 12 − 5 − 35
14 − 20 4 17 0 0
20 − 28 4 24 7 28
28 − 38 3 33 16 48
38 − 40 1 39 22 22
Total 40 − 181
7. From the table, we obtain
Therefore, the mean number of days is 12 days for which a
student was absent.
8. The "mode" is the value that occurs most
often. If no number is repeated, then there is
no mode for the list.
9. Limitation:-Could be very far from the actual middle of the
data. The least reliable way to find the middle or average of
the data.
Uses:- the mode when the data is non-numeric or when
asked to choose the most popular item.
10. Example:-
The given distribution shows the number of runs
scored by some top batsmen of the world in one-
day international cricket matches.
Find the mode of the data.
Runs scored Number of batsmen
3000 − 4000 4
4000 − 5000 18
5000 − 6000 9
6000 − 7000 7
7000 − 8000 6
8000 − 9000 3
9000 − 10000 1
10000 − 11000 1
11. Solution:-
From the given data, it can be observed that the maximum
class frequency is 18, belonging to class interval 4000 −
5000.
Therefore, modal class = 4000 − 5000
Lower limit (l) of modal class = 4000
Frequency (f1) of modal class = 18
Frequency (f0) of class preceding modal class = 4
Frequency (f2) of class succeeding modal class = 9
Class size (h) = 1000
Therefore, mode of the given data is 4608.7 run
12. The "median" is the middle value
in the list of numbers. To find
the median, your numbers have
to be listed in numerical order,
so you may have to rewrite your
list first.
13. LIMITATION: If the gap between some numbers is large,
while it is small between other numbers in the data, this can
cause the median to be a very inaccurate way to find the
middle of a set of values.
Uses:- the median to describe the middle of a set of data
that does have an outlier.
14. Example:-
A life insurance agent found the following data for distribution
of ages of 100 policy holders. Calculate the median age, if
policies are given only to persons having age 18 years
onwards but less than 60 year.
Age (in years) Number of policy holders
Below 20 2
Below 25 6
Below 30 24
Below 35 45
Below 40 78
Below 45 89
Below 50 92
Below 55 98
Below 60 100
15. Solution:-
Here, class width is not the same. There is no requirement of
adjusting the frequencies according to class intervals. The given
frequency table is of less than type represented with upper class
limits. The policies were given only to persons with age 18 years
onwards but less than 60 years. Therefore, class intervals with
their respective cumulative frequency can be defined as below.
Age (in years)
Number of policy
holders (fi)
Cumulative
frequency (cf)
18 − 20 2 2
20 − 25 6 − 2 = 4 6
25 − 30 24 − 6 = 18 24
30 − 35 45 − 24 = 21 45
35 − 40 78 − 45 = 33 78
40 − 45 89 − 78 = 11 89
45 − 50 92 − 89 = 3 92
50 − 55 98 − 92 = 6 98
55 − 60 100 − 98 = 2 100
Total (n)
16. From the table, it can be observed that n = 100.
Cumulative frequency (cf) just greater than is 78, belonging to
interval 35 − 40.
Therefore, median class = 35 − 40
Lower limit (l) of median class = 35
Class size (h) = 5
Frequency (f) of median class = 33
Cumulative frequency (cf) of class preceding median class = 45
Therefore, median age is 35.76 years.
17. Also known as an ogive, this
is a curve drawn by plotting
the value of the first class
on a graph. The next plot is
the sum of the first and
second values, the third plot
is the sum of the first,
second, and third values, and
18. Example:-
During the medical check-up of 35 students of a class, their
weights were recorded as follows:
Weight (in kg) Number of students
Less than 38 0
Less than 40 3
Less than 42 5
Less than 44 9
Less than 46 14
Less than 48 28
Less than 50 32
Less than 52 35
Draw a less than type ogive for the given data. Hence obtain the
median weight from the graph verify the result by using the
formula.
19. Weight (in kg)
upper class limits
Number of students
(cumulative frequency)
Less than 38 0
Less than 40 3
Less than 42 5
Less than 44 9
Less than 46 14
Less than 48 28
Less than 50 32
Less than 52 35
Solution:-
The given cumulative frequency distributions of less than type are
Taking upper class limits on x-axis and their respective cumulative
frequencies on y-axis, its ogive can be drawn as follows.
20. Here, n = 35
So, = 17.5
Mark the point A whose ordinate is 17.5 and its x-coordinate is
46.5. Therefore, median of this data is 46.5.
21. It can be observed that the difference between two consecutive
upper class limits is 2. The class marks with their respective
frequencies are obtained as below.
22. Weight (in kg) Frequency (f) Cumulative
frequency
Less than 38 0 0
38 − 40 3 − 0 = 3 3
40 − 42 5 − 3 = 2 5
42 − 44 9 − 5 = 4 9
44 − 46 14 − 9 = 5 14
46 − 48 28 − 14 = 14 28
48 − 50 32 − 28 = 4 32
50 − 52 35 − 32 = 3 35
Total (n) 35
The cumulative frequency just greater than is 28,
belonging to class interval 46 − 48.
Median class = 46 − 48
Lower class limit (l) of median class = 46
23. Frequency (f) of median class = 14
Cumulative frequency (cf) of class preceding median class = 14
Class size (h) = 2
Therefore, median of this data is 46.5.
Hence, the value of median is verified.
24. Mean of grouped data can be found by:-
With the assumption that frequency of class is
centered at its mid point, called class mark.
25. Mode of grouped data can be found by following
formula:
The cumulative frequency of a class is the
frequency obtained by adding the frequencies of
all the class preceding the given class.
Median of grouped data is formed by
following formula:
26. Representation of cumulative frequency
distribution graphically is done through
cumulative frequency curve or an ogive of less
than type or more than type.
The median of grouped data can be obtained
graphically as x-coordinate of the point of
intersection of two ogives.